The tropical theory is not merely an analogue of the algebraic theory. A process known as tropicalization turns an algebraic curve into a graph whose combinatorial invariants encode various geometric properties of the curve.
Most notably, Baker's specialization lemma states that the rank of divisors may only increase under this process [1]}, an observation at the heart of various recent developments
in the geometry of curves
[2]}, [3]}, [4]}, [5]}.
